1. Field of the Invention
The present invention relates to a measurement technique for measuring physical values on the surface (optical physical values such as refractive index, reflectivity, and absorptivity, and values indicating surface shape such as surface roughness, surface temperature, thickness of thin film, etc.) of a material in the process of manufacture by detection of thermal radiation energy having two or more different wavelengths.
2. Prior Art
In the process of manufacturing semiconductor material, metallic material, and the like, various reactions such as oxidation, galvannealing, and vapor deposition occur on the surface of the material in process either artificially or naturally and thereby vary physical properties of the material surface greatly on account of such reactions. However, the sensing of the interior of the material is very difficult. It is not preferred from a practical point of view to attach many sensors to the material in order to obtain various data. Therefore, the surface temperature is selected as the most influential parameter from the physical, values or state values, and the surface temperature is utilized for process control as the value for predicting changing status in on-line sensing or in theoretical calculation. For example, in a process of forming oxide film on a silicon wafer, correlative data between the heat pattern of the oxidation process furnace and physical properties of oxide film are measured off-line to obtain many off-line data in advance. The furnace temperature is controlled based on such data. (Although it is desirable to execute control of the surface temperature, indirect control according to the furnace temperature is executed because of difficulty in the on-line sensing.)
For the on-line material surface temperature sensing, there are two temperature sensing techniques: contact method and non-contact method. In the contact temperature sensing method using a thermocouple, thermistor, etc., many problems occur such as: the measurable temperature range is limited, the position where temperature can be measured is limited to the point of sensing, and contamination of the material occurs (addition of impurities thereto) by the contact. Therefore, the processes to which this method is applicable are limited. In the non-contact temperature measuring method, there is "radiation thermometry". This is a practical technique in the process line of metallic materials such as iron, steel and aluminum, and there is a radiation thermometer as a product on the market.
For the process line of a metallic material as described above, there already is developed a technique to measure the surface temperature in a non-contact manner. However, for the process of manufacturing a semiconductor or a new material, such a measuring technique is still in the studying stage. Although various efforts are being made to develop surface temperature measuring techniques, there has not yet been developed any effective technique.
It is reported, for example, in Watanabe, et. al., "Measurement of Wafer Temperature within Semiconductor Heat Treatment Apparatus by Radiation Thermometer", The Transactions of the Japanese Institute of Measurement and Automatic Control Engineers, Vol. 25, No. 9, pp. 925-931 (1989), that it has at last been made possible to apply radiation thermometry to a manufacturing process, to which furnace temperature control has hitherto been applied, by using fiber optics and prisms. From the fact that studies recently made public are on such a stage, it is the present state that there has not been developed any effective technique of on-line radiation thermometry in the field of processing semiconductors.
On the other hand, there are widely used radiation thermometers with the radiation thermometry technique applied thereto for measuring the surface temperature of hot matters. There are two types of such radiation thermometers, i.e., single-color thermometers using a single wavelength for the measurement and two-color thermometers using two wavelengths. Even the two-color thermometer using two wavelengths, not to mention the single-color thermometer, produces a great measurement error when the emissivity of the object of measurement changes.
More specifically, there is no problem with the temperature measurement accuracy of the two-color thermometer when spectral emissivities for two wavelengths are virtually equal or have constant proportionality therebetween. However, the surface condition of a hot matter suddenly changes due to oxidation reaction caused thereon, and when the spectral emissivities deviate from the aforesaid relationship, the measurement accuracy decreases extremely. The error in the single-color radiation thermometer becomes much greater. Therefore, there is a demand for a temperature calculation method for the two-color thermometer responding to changes in the spectral emissivity. Studies for providing such a method are being made, and an improved two-color thermometer is being contemplated for use even where the emissivity changes.
There is a method disclosed in Japanese Patent Publication No. 3-4855 and a TRACE (Thermometry Reestablished by Automatic Compensation of Emissivity) method disclosed in Tanaka and D. P. Dewitt, "Theory of a New Radiation Thermometry Method and an Experimental Study Using Galvannealed Steel Specimens", The Transactions of the Japanese Institute of Measurement and Automatic Control Engineers, Vol. 25, No. 10, pp. 1031-1037 (October 1989). Since both of the above calculation methods are substantially the same, the former will be described below. The spectral emissivity for radiation energy (light wave) emitted from a material in process is obtained by using Wien's approximation law. When wavelengths are .lambda..sub.1 and .lambda..sub.2, the emissivities are given by the following expressions (1) and (2). By eliminating temperature T from these expressions, expression (3) can be obtained. (Symbols used in these expressions will be mentioned below.)
Measurement wavelength: .lambda..sub.1 [.mu.m] PA1 Spectral emissivity for a measurement PA1 wavelength: .epsilon..sub.i [.mu.m] PA1 True temperature of the hot matter surface: T [K] PA1 Brightness temperature of the hot matter surface at a wavelength .lambda..sub.i : Si [K) PA1 Planck's second radiation constant: C2 (1.4388.times.10.sup.4) [.mu.M.multidot.K] EQU .epsilon..sub.1 =exp[(C2/.lambda..sub.1){(1/T)-(1/S1)}] (1) EQU .epsilon..sub.2 =exp[(C2/.lambda..sub.2){(1/T)-(1/S2)}] (2) EQU .epsilon..sub.1.sup..lambda.1 /.epsilon..sub.2 =exp[(C2{(1/S2)-(1/S1)}](3)
The left side of the expression (3) is the ratio between "the wavelength power, or involution, of spectral emissivities", which, will hereinafter be called "emissivity involution ratio" for simplicity. The old two-color radiation thermometer measures temperature on the assumption that the ratio between spectral emissivities (.epsilon..sub.1 /.epsilon..sub.2) is "1" or a constant. Because it does not respond to changes in the spectral emissivities, it produces a great measurement error. (The ratio between emissivities will hereinafter be called "emissivity ratio".)
In Japanese Patent Publication No. 3-4855, the correlative function "f" of the spectral emissivity ratio (.epsilon..sub.1 /.epsilon..sub.2) to the emissivity involution ratio is decided in advance by measurement. To be concrete, if radiation thermometry and true temperature measurement are performed at the same time by using, for example, a thermocouple, the spectral emissivity is obtained. By using such data, the spectral emissivity ratio and the emissivity involution ratio can be obtained. Hence, the correlative function f can be obtained from them. Further, since the brightness temperatures S1 and S2 can be obtained as outputs of the two-wavelength detector, the value of the above emissivity involution ratio can be obtained by calculating the right side of expression (3). Accordingly, in the temperature measurement, the brightness temperatures are measured and the emissivity ratio is obtained according to the following expression (4) from the emissivity involution ratio calculated according to the above expression (3) by using the correlative function f. The temperature T is obtained by making calculations according to the following expression (5). EQU .epsilon..sub.1 /.epsilon..sub.2 =f(.epsilon..sub.1.sup..lambda.1 /.epsilon..sub.2.sup..lambda.2) (4) EQU T=(.lambda..sub.2 -.lambda..sub.1)/{(.lambda..sub.1 .lambda..sub.2 /c2)1n(.epsilon..sub.1 /.epsilon..sub.2)+(.lambda..sub.2 /s1)-(.lambda..sub.1 /s2).} (5)
However, when the above described prior art is applied to surface temperature measurement in surface processing of silicon semiconductors, such as the formation of a surface thin film, problems arise such that the function "f" in expression (4) becomes very complicated and the calculation becomes difficult or, if it is simplified by approximation, an error is produced. In the surface process of the silicon semiconductor, the thin film of the surface changes. Therefore, when attempting to measure the surface temperature, the emissivity varies greatly because of optical interference in the thin film. This makes practical radiation thermometry difficult.
In the manufacturing process of semiconductor materials, metallic materials, and the like, although it has been desired that the surface physical properties of the materials in process are measured and on-line process control is thereby executed, such control is not practiced in reality. Further, since surface physical properties change with time and also are closely related with the temperature of the material, it becomes necessary that the surface physical properties and the surface temperature are measured at the same time on an on-line basis. However, it has hitherto been impossible to simultaneously measure the surface physical properties and the surface temperature in the same position of the material.
Further, when the measurement method by the two-color thermometer using the above expressions (1) to (5) is applied to thermometry of a hot matter whose surface condition changes with the progress of oxidation reaction or the like, temperature measurement with high accuracy can be attained provided that the measurement wavelengths used are "insensitive" to changes of the surface status. However, when the spectral emissivities of the selected wavelengths are sensitive to the change in the surface condition, a problem arises that greatly decreases the measurement accuracy.
More specifically, as a concrete example, when the spectral emissivities of selected wavelengths sensitively change responding to changes in the surface status of a hot matter, in one case, the surface oxidizes and forms a translucent (to the measurement wavelength) oxide film on the surface. In such a case, optical interference takes place in the translucent film formed on the surface and the spectral emissivity is thereby greatly reduced.
Makino et. al. gives account of such a phenomenon of a sudden change of emissivity in, for example, "Heat Transfer 1986", Vol. 2, Hemisphere (1986) pp. 577-582, on the basis of experiments and model calculations based on optical interference theories, that a drop (valley) appears in the spectral emissivity (reflectivity) spectrum at a short-wavelength zone when surface oxidation occurs and the sudden change is confirmed to be a characteristic change of the valley moving toward the longer-wavelength side as the oxidation progresses.
FIG. 65 to FIG. 69 are diagrams schematically showing an example of such a characteristic change in a spectral emissivity spectrum. Referring to the diagrams, the axis of abscissas represents the spectral wavelength .lambda. and the axis of ordinates represents the emissivity .epsilon.. Further, the portion indicated by "valley" is the valley in the spectral emissivity spectrum.
FIG. 65 to FIG. 69 show changes in the spectral emissivity spectrum of the surface as an oxide film is progressively formed on a surface of a metal such as stainless steel.
FIG. 65 shows a spectrum in a low temperature state when no oxide film is formed. FIG. 66 shows a spectrum in an intermediate temperature state when an oxide film is not yet formed. FIG. 67 shows a spectrum in an intermediate temperature state when an oxide film has started to form. FIG. 68 shows a spectrum in a state of the material at the same temperature and having the oxide film developed thereon, and FIG. 69 shows a spectrum in a state of the material heated to a high temperature and having a thick oxide film formed thereon.
The occurrence of the valley is considered chiefly attributable to optical interference caused by an oxide film, and the above introduced Makino et. al. obtained spectral emissivity spectra through model calculation based on interference theories and report that results of the calculation and the experimental results concur well with each other.
Accordingly, the change in the spectral emissivity spectrum occurs because radiation energy of a spectral wavelength band on the order below the thickness of the oxide film is selectively trapped in the oxide film. More specifically, remarkable energy attenuation is produced because radiation of a uniquely selected wavelength band produces interference or multiple reflection in the oxide film and the valley moves from a short wavelength side to a long wavelength side because the uniquely selected wavelength band moves as the oxide film becomes thicker.
Since the emissivity ratios change as the spectral emissivity spectra change with the passage of time as described above, it is natural that measurement errors are produced in the old type two-color radiation thermometer. Measurement errors are equally produced even in the above described improved type two-color thermometer because of difficulty in the calculation of expressions used therein.
The calculation in the improved type two-color thermometer using nearby two wavelengths .lambda..sub.1 and .lambda..sub.1x (.lambda..sub.1 &lt;.lambda..sub.1x) requires that correlation of the two spectral emissivities .epsilon..sub.1 and .epsilon..sub.1x is determined as a regression function in advance from experimental data on an off-line basis. Therefore, the regression procedure falls into difficulty that will be briefly described below.
Supposing that actual measured data of spectral emissivities .epsilon..sub.1 and .epsilon..sub.1x are obtained while the movement of the valley from the short wavelength side to the long wavelength side is taking place as in the spectral emissivity spectrum described above, the correlation of the emissivity .epsilon..sub.1 and the .epsilon..sub.1X changes as "positive correlation".fwdarw."negative correlation".fwdarw."positive correlation".
This will be understood easily if the changes in the values of the emissivities .epsilon..sub.1 and .epsilon..sub.1x corresponding to the nearby two wavelengths .lambda..sub.1 and .lambda..sub.1x are traced in FIG. 65 through FIG. 69. More specifically, when the low wavelength portion of the "valley" in the diagrams (the portion where the spectral gradient is negative) comes between the wavelengths .lambda..sub.1 and .lambda..sub.1x, the relative magnitude between the spectral emissivities .epsilon..sub.1 and .epsilon..sub.1x is reversed and the positiveness and the negativeness of the correlation are reversed.
The situation will be concretely shown in FIG. 70 and FIG. 71. The correlation before passing the valley (FIG. 70) and after passing the valley (FIG. 71) is obviously completely reverse.
Tanaka et. al., "Studies on Iron Manufacture", No. 339 (1990) pg. 63-67, shows the graph .epsilon..sub.1 vs. .epsilon..sub.2 is not one-valued, but rather forms a loop, as schematically shown in FIG. 72. This loop is supposedly due to radiation interference occurring in the oxide film.
Thus, the occurrence of some measurement error is unavoidable even in the improved type two-color thermometer because the correlative regression graph between the emissivities .epsilon..sub.1 and .epsilon..sub.1x cannot be simply determined.
When temperatures of stainless steel plate (SUS 304) were actually measured with the above-described improved type two-color thermometer while surface oxidation was in progress, the maximum measurement error in the domain of galvannealing temperature around 600.degree. C. was approximately 15.degree. C. and the standard deviation was approximately 5.degree. C.
In the course of the development of surface oxidation or surface galvannealing and the change in surface physical properties as described above, the temperature is an influential process parameter in the steel manufacturing process control. Therefore, it is a serious problem that there is an error in the measurement value obtained by radiation thermometry and hence there are demands for a more accurate thermometer. The desired measurement accuracy is a temperature measurement error of .+-.5.degree. C. (maximum error is within 5.degree. C.).
Accordingly, there are demands for the development of a radiation thermometer having higher measurement accuracy than the above improved type two-color thermometer.
Therefore, in order to overcome the above described difficulties in the improved type two-color thermometer, it is contemplated to use three or more wavelengths for the measurement so as to form a number of combinations of two wavelengths out of them. Then, the same process as with the improved type two-color thermometer is performed for each combination of two wavelengths to measure temperature.
However, in such methods using three or more measurement wavelengths and increasing the number of combinations of two wavelengths, there still are the following problems.
To simplify the explanation, an example will be considered where the measurement wavelengths are three (i.e., .lambda..sub.1,.lambda..sub.2, and .lambda..sub.3 when .lambda..sub.1 &lt;.lambda..sub.2 &lt;.lambda..sub.3), and the combinations of the two wavelengths are made for convenience to be (.lambda..sub.2, .lambda..sub.3) and (.lambda..sub.1,.lambda..sub.2).
From brightness temperatures S1, S2, and S3 measured for the wavelengths .lambda..sub.1, .lambda..sub.2, and .lambda..sub.3, two combinations (S2, S3) and (S1, S2) corresponding to the above combinations of wavelengths are made. Emissivity involution ratios and .epsilon..sub.3.sup..lambda.3 /.epsilon..sub.2.sup..lambda.2 and .epsilon..sub.2.sup..lambda.2 /.epsilon..sub.1.sup..lambda.1 are calculated using expressions corresponding to the above-mentioned expression (3). Correlative functions f1 and f2 corresponding to the above-mentioned expression (4) are applied to the above emissivity involution ratios to obtain emissivity ratios .epsilon..sub.3 /.epsilon..sub.2 and .epsilon..sub.2 /.epsilon..sub.1.
However, if it is assumed that the function f1 is given according to the graph shown in FIG. 73 because an oxide film is formed on the surface of the object of measurement, the emissivity ratio takes on two values A1 and A2 when the value of the emissivity involution ratio obtained from the expression corresponding to the expression (3) is AO. On the other hand, if it is assumed that the function f2 is given according to the graph shown in FIG. 74, three values B1, B2, and B3 are obtained as the emissivity ratios corresponding to the calculated value B0 of the emissivity involution ratio.
Therefore, when the number of measurement wavelengths is simply increased and applied to the above described improved-type two-color thermometer, an expression corresponding to the above-mentioned expression (5) must be used to calculate temperatures for the five points (i.e., the two emissivity ratios A1 and A2 and the three emissivity ratios B1 to B3). A search must be made for those temperatures agreeing with each other from the temperatures obtained from A1 and A2 and the temperatures obtained from B1 to B3, to thereby determine the agreeing temperature as the true surface temperature. Accordingly, there is a problem that the calculation process for the search is complex.
As an example of prior art radiation thermometry, there is disclosed in U.S. Pat. No. 4,417,822, a laser additionally used. The reflectivity for the laser beam from the surface of the object of measurement is used for compensating for the emissivity. This method has a disadvantage in that the apparatus becomes complex and expensive because it employs a laser. Further, it is required to obtain off-line data for the measurement of the reflectivity for the laser beam. However, the data involves intricate factors related to an optical scattering phenomenon taking place on the surface. It is therefore questionable whether the off-line data can be used in the on-line measurement. Besides, since an error is produced in the on-line measurement value of the reflectivity, the error in the temperature measurement becomes great.
In U.S. Pat. No. 4,561,786, a radiation thermometrical art is disclosed using an apparatus as shown in FIG. 75.
In this art, a radiation wave is converged by a lens 813 and separated by a rotating filter 815 to obtain two-color measurement wavelengths. Outputs for the two-color wavelengths are detected by a detector 811 and secondary calculation is performed on the outputs to obtain "ratio" and "difference" therebetween. By utilizing such calculation values, the temperature calculation is performed for practical use.
Referring to FIG. 75, reference numeral 851 denotes a division block for performing a division between outputs W1 and W2 of sample and holding circuits 845 and 847. Namely, its output constitutes the "ratio". Reference numeral 859 denotes a differential amplifier for performing a subtraction between outputs of sample and holding circuits 855 and 857. The output constitutes the "difference". Reference numerals S1 to S4 denote timing signals for synchronizing the rotational position of the rotating filter 815 with the controlling system. 817 denotes a spectroscopic filter for the first wavelength and 819 denotes a spectroscopic filter for the second wavelength 841 and 843 denote amplifiers.
For the outputs from the division block 851 and the differential amplifier 859, linearizing networks 853 and 861 and resistance values R1, R2, R3, and R4 are set up after adjusting them in accordance with each object of measurement. The calculation temperature value is displayed on a meter 875.
In this method, adjustments of the linearizers 853 and 861, and resistors R1 to R4 are determined in a trial and error manner. Accordingly, the calculation method that has come into existence as a result of trial and error is not based upon theories. In fact, there is no theoretical description given.
According to this method, it is stated that temperature measurement on aluminum with surface change progressing thereon can be made with high accuracy (.+-.5.degree. C.). However, to obtain such high accuracy, a long trial and error period is required (data for setting up are not disclosed).
Because the apparatus using the above-described method has no theoretical foundation, a long period of trial and error will be required for measuring materials other than aluminum. It therefore has no general applicability.
From the standpoint of those who control manufacturing processes, such a system is preferable when not only the surface temperature is measured but also the changes in other surface physical properties are monitored (sensed) and process control is executed through feedback control with such monitored values. Surface physical properties of materials are not only directly affected by such factors as surface roughness, surface reflectivity (emissivity), surface absorptivity, and refractive index, but also greatly affected indirectly by such physical properties within the material such as oxide film thickness, galvannealed film thickness, evaporation-deposited film thickness, electric conductivity, and boundary (inter-film) refractive index. More specifically, surface physical properties are determined by the physical properties of the substance produced after reactions have taken place in the vicinity of the surface and the physical properties related to the interface between the produced substance and the base material. It may safely be said that the surface properties cannot be assumed from the direct physical properties of the surface itself. Of course, the surface properties are greatly affected by conditions of the material in process such as surface temperature, internal temperature, and their distribution.
Thus, in accurately obtaining surface physical properties of a material in process, it is preferred that not only the surface physical properties but also changes in the physical property and changes in the state within the material are sensed. For example, in the above described oxide film forming process on a silicon wafer, control of the surface physical property is only executed indirectly by controlling the furnace temperature, while blind control (without any on-line sensor) is executed as to the actual condition of the physical property of the oxide film. Naturally, statistical process errors occur. Because of difficulty of the sensing, such "blind" control is prevalent throughout general semiconductor processes and is responsible for low yield rate of semiconductors. Such situations are present not only in the field of processing semiconductors but also in the fields of processing high tech materials such as ceramics and superconductive materials. In order to improve such "blind" control, which executes indirect control of physical properties by temperature to increase the yield rate in the process, it is desired that on-line monitoring (sensing) capable of measuring changes in surface physical property of material in process is realized.